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metallic glass matrix composites by pre-deformation
Materials and Design 86 (2015) 266–271
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Plasticity improvement for dendrite/metallic glass matrix composites by pre-deformation X.H. Sun a,b, Y.S. Wang a,b, J. Fan a, H.J. Yang c, S.G. Ma d, Z.H. Wang d, J.W. Qiao a,b,⁎ a
Laboratory of Applied Physics and Mechanics of Advanced Materials, College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China Key Laboratory of Interface Science and Engineering in Advanced Materials, Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan 030024, China d Institute of Applied Mechanics and Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, China b c
a r t i c l e
i n f o
Article history: Received 11 May 2015 Received in revised form 8 July 2015 Accepted 19 July 2015 Available online 26 July 2015 Keywords: Metallic glass Composite Improved plasticity Tensile pre-deformation Shear bands Young's modulus
a b s t r a c t The mechanical properties of in-situ metallic glass matrix composites (MGMCs) are investigated by tensile predeformation, followed by compression. The pre-deformation is utilized to exploit notable increases in plasticity, accompanied by slight increases in the compressive strength, and the deformation mechanisms are explored. The increased free volumes in the glass matrix after tensile pre-deformation contribute to the decrease of the Young's modulus of the glass matrix and lead to the increase in the stress concentration, promoting multiplication of shear bands. When the Young's modulus of the glass matrix matches that of the dendrites, the plasticity of insitu dendrite-reinforced MGMCs is the optimized. Matching Young's modulus opens a door to design the MGMCs with excellent plasticity and remarkable work-hardening capability. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Plastic deformation in bulk metallic glasses (BMGs) manifests through the strain localization shearing into narrow bands, which are often referred to as shear bands [1,2]. The shear bands, which have an unhindered propagation in monolithic BMGs, yield negligible tensile ductility. Recently, great interest arises in BMGs as structural materials, since they exhibit superior mechanical properties, such as high strength, large elastic limits, and high corrosion resistance [3]. However, a widespread acceptance of monolithic BMGs in engineering applications is limited by their poor ductility under loading at room temperature. One way to alleviate this problem is that the crystalline phases are insitu introduced to effectively generate multiple shear bands and impede the rapid propagation of shear bands [4,5]. To date, the dimension for lightweight in-situ dendrite-reinforced metallic glass matrix composites has reached a centimeter scale and even larger for systems such as Ti–Zr–V–Cu–Be [6], Ti–Zr–Ni–Cu–Be [7], and Ti–Zr–Cu–Ni–Al [8]. These ingots are large enough to be used as potential structural materials in various application fields. It should be noted that the improvement of plasticity and the enhancement of work-hardening capacity are badly needed for dendrite-reinforced metallic glass matrix composites (MGMCs). ⁎ Corresponding author at: Yingze West Street 79 Taiyuan, Shanxi Province, 030024, China. Tel.: +8613643467172. E-mail address: [email protected] (J.W. Qiao).
http://dx.doi.org/10.1016/j.matdes.2015.07.109 0264-1275/© 2015 Elsevier Ltd. All rights reserved.
For in-situ MGMCs, the deformation mechanisms should be fully understood before actual service. After introducing the secondary phases in the glass matrix, both phases in the composites are under the multi-axial stress state during the deformation. The concentrated stress, induced by the secondary phases, can interact with the stress field, originated from propagating shear bands, leading to the multiplication, branching, and deflection of shear bands. As a result, shear bands in these MGMCs are characterized to be dense, short, and wavy [9]. The profuse shear bands could accommodate more strain energy, resulting in effective toughening. For monolithic BMGs, introducing structural inhomogeneity can produce residual stress, and then, the pre-existed shear bands and free volumes improve the plasticity [10–12]. Zhang et al. [10] have pointed out that the plasticity of Vitreloy 1 BMGs was improved by introducing compressive residual stress on the sample surface by shot-peening. Cao et al. [11] have reported that pre-existed properly-spaced soft inhomogeneities can stabilize shear bands and lead to tensile ductility, and the effective intersection of shear bands in conjugated directions resulted in obvious work hardening. Haruyama et al. [12] put forward that coldrolled BMGs exhibited volume dilatation, caused by the generation of free volumes. Generally, the heterogeneities can manipulate nucleation and propagation of shear bands, which is responsible for the enhanced plasticity of BMGs [13]. Hofmann et al. [14] have reported that the shear bands generated during rolling provided nucleation sites for the new shear bands generated during tension. The deformation mechanisms of β-Ti solid solution (dendrites) are based on the dislocation
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multiplication and slip [15–18]. The work-hardening capacity, associated with homogeneous deformation, is highly dependent on the large plastic deformation of both the dendrites and the metallic glass matrix [19]. Based on the above micromechanisms, multiplication, branching, and deflection of the shear bands are crucial to improve the plasticity. The pre-deformation not only increases the free volumes in the glass matrix [12,20–25], but also the dislocation density within the crystalline dendrites increases [15–18]. Recently, Ke et al. reported [26] that the Zr46.75Ti8.25Cu7.5Ni10Be27.5 BMG exhibited volume dilatation of up to 0.2% after compressive creep of the as-cast sample at a yield stress of 80%, and this phenomenon is attributed to the generation of a great amount of free volumes. The increased free volumes make the Young's modulus of the glass matrix decrease [20,24,25], resulting in the Young's modulus of the glass matrix and dendrites being approaching, since the crystalline dendrites have a lower Young's modulus than the glass matrix. The aim of this study is to investigate the contribution of matching the Young's modulus between the glass and dendrite phases to the plasticity of in-situ dendrite-reinforced MGMCs. 2. Experimental procedures Ingots of a nominal composition: Ti48Zr18V12Cu5Be17 (at.%) were prepared by arc-melting a mixture of the elements Ti, Zr, V, Cu, and Be with high purity (N99.9%) under a Ti-gettered argon atmosphere. Two cylindrical rods with a diameter of 2 mm and 6 mm were prepared via suction casting into a copper mold, respectively. The phases of the samples were checked by X-ray diffraction (XRD) in a Philips APD-10 diffractometer with Cu Ka radiation. The pre-deformation experimental procedures were schematically shown in Fig. 1. The dog-bone-like tensile samples with a nominal diameter of 2 mm and a length of 15 mm were machined from the as-cast rods with 6-mm diameter. Sample A with an aspect ratio of 2:1 was cut from the gage section of as-cast samples, and their ends were prepared and polished to ensure the parallelism. The tensile samples were drawn to the stage of work hardening and the failure at room temperature at a constant strain rate of 5 × 10−4 s−1, respectively. And then, samples B and C with an aspect ratio of 2:1 were cut from the deformed samples within the gage section, respectively, as shown in Fig. 1. Sample D with an aspect ratio of 2:1 was directly cut from as-cast bars with a diameter of 2 mm. The compressive tests were carried out on samples A, B, C, and D at a strain rate of 5 × 10−4 s−1. The microstructures of as cast samples and the fracture
Fig. 1. The experimental procedure schematic diagram.
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surfaces after compression were investigated by scanning electron microscopy (SEM). 3. Results 3.1. Microstructures The microstructures of samples D and A are illustrated in Fig. 2(a) and (b), respectively. The SEM images of the cross-sections for samples B and C are very similar to that of sample A (not shown). The dense small dendrites are homogeneously embedded in the glass matrix, as shown in Fig. 2(a). From the magnified image in the inset of Fig. 2(a), the average diameter of the dendritic arms of sample D is less than 1 μm. However, that of samples A, B, and C are the same with a value of ~ 2 μm, as shown in Fig. 2(b). The size of the dendritic arm can be controlled by the cooling rate during casting [27]. The dendrite's volume fractions in samples A, B, C, and D are all ~46% by analyzing the contrast of the SEM image, and similar results have been observed by Jeon et al. [28]. X-ray diffraction patterns of the composites (not shown here) indicate that the dendritic phase is a β-Ti solid solution with a body-centered cubic crystal structure. 3.2. Mechanical behavior 3.2.1. Tensile behavior Fig. 3 displays the tensile stress–strain curve of the present composites. After yielding, the MGMCs exhibit not only high tensile strength of 1422 MPa, but also remarkable work-hardening capacity. The following softening dominates until the final fracture at a fracture strain of ~5.9%.
Fig. 2. The SEM micrographs of the as-cast composites with a diameter of 2 mm and 6 mm in (a) and (b), respectively. The inset of (a) being magnified micrograph of as-cast composite with a diameter of 2 mm.
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X.H. Sun et al. / Materials and Design 86 (2015) 266–271 Table 1 Summary of compressive yielding strength (σy), elastic strain (εy), ultimate compressive strength (σmax), and total strain to failure (εf) for the present MGMCs. Sample
A B C D
σy
εy
σmax
εf
MPa
%
MPa
%
1675 1493 1646 2026
1.98 1.93 1.96 1.99
2585 2747 2697 2815
22.9 34.6 30.3 19.2
A: Φ6 → 2 casting. B: Φ6 → 2 hardening. C: Φ6 → 2 softening. D: Φ2 casting.
4. Discussion Fig. 3. The tensile true stress–strain curve of as-cast Ti48Zr18V12Cu5Be17 sample. The samples in pictures (i), (ii), and (iii) being in a state of casting, work hardening, and softening, respectively. The inset (iv) showing the lateral surface near the necked region after tension failure.
Macroscopic necking can be observed in the inset (iii), in agreement with the large tensile ductility. Samples A, B, and C are machined from the tensile specimens, as exhibited in the insets of (i), (ii), and (iii) in Fig. 3, respectively. The inset (iv) in Fig. 3 shows the lateral surface near the necking region after failure. Multiplication of shear bands within the glass matrix, indicated by the dark arrows, together with some cracks, indicated by the light arrows, is consistent with the distinguished tensile ductility.
3.2.2. Compressive behavior Fig. 4 represents the compressive stress–strain curves of samples A, B, C, and D. Initially perfectly elastic deformation is followed by the obvious macroscopic plastic deformation. Summary of compressive mechanical properties is listed in Table 1. Sample D possesses the highest yielding strength of 2026 MPa, but the lowest plasticity of 19.2%. Sample A exhibits lower yielding strength of 1675 MPa and larger plasticity of 22.9%, similar results that improved plasticity at the expense of yielding stress have been found in samples DH1, DH2, and DH3 [4]. Compared with sample A, the difference exists in yielding stress, and the fracture strain of sample C is 32% higher than that in sample A. Sample B at a state of work hardening has larger plasticity but lower yielding stress than sample C at a state of softening. The slight increases in the ultimate compressive strength for samples B and C with the pre-tension deformation, and the analogical results are found in pre-rolled MGMCs [14].
Most monolithic BMGs exhibit catastrophic failure with brittleness upon whether tensile or compressive loadings at room temperature, as dominated by individual shear bands, since large plasticity is usually correlated to profuse shear bands [11–15,29]. For the conventional crystalline samples, the macroscopic plasticity is closely related to the multiplication of dislocations [18]. As far as the current composite is concerned, the deformation mechanisms of the glass matrix and crystalline dendrites are coupled upon quasi-static compression. Different sizes of the dendrites lead to different mechanical properties, and the size of the dendrites plays an important role in gaining the ductility of in-situ MGMCs [4,6,30]. The crystalline phases can absorb the strain energy during the deformation, contributing to the improved plasticity. Besides, the propagation of shear bands can be arrested by the ductile crystalline phases, the instability can be suppressed, and the significantly improved toughness of MGMCs at room temperature prevails. However, not all the dendrites, dispersed in metallic glass matrix, can initiate and arrest shear bands, and finally lead to the formation of profuse shear bands. The size of the dendrites is too small to retard the rapid propagation of shear bands, accompanied by a decreasing plasticity [27,31]. As the stress is increased, more shear transformation zones (STZs) within the glass matrix will be activated. When the stress reaches a critical value, yielding occurs to produce plastic deformation, immediately followed by the initiation of shear bands [32]. At the plastic deformation stage, the shear bands initiate in the glass matrix, the larger stress concentration will stimulate more shear bands near the interface. As a result, the plasticity of the composites is enhanced. But for the present sample D, the dendrites are so small that the maximum stress concentration happens at the elastic stage [30], while the glass matrix is still under elastic deformation and strong enough to impede the initiation of shear bands. At the plastic stage, the stress concentration becomes weak, which cannot induce generations of shear bands. Macroscopically, sample D is less plastic than sample A with large-sized dendrites, and similar results have been obtained in in-situ Ti-based [33] and Zr-based MGMCs [27]. The ductile dendrites are confined by the glass matrix, which experience a multi-axial stress state and produce inhomogeneous plastic deformation upon compression [34]. The strong interfacial bonding effectively transfers the stress to the matrix [33]. Therefore, the stress concentration within dendrites produced by plastic deformation will lead to the initiation of shear bands in the glass matrix near the interface, and the stress concentration factors of the dendrites will affect the initiation of shear bands. The average stress concentration factors of the dendrites can be described as follows [35]: cd ¼
Fig. 4. The compressive stress–strain curves of the present samples with different pretreatments.
Ed ½ f v þ ð1−f v ÞβðEd −Em Þ þ Em
ð1Þ
where fv represents the volume fraction of the dendrites with a value of 0.46, cd represents the average stress concentration factors of the
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dendrites, β is the material constant, which is calculated through β ¼ 8−10vd 15ð1−vd Þ ,
and vd is the Poisson's ratio of the dendrites with a value of
0.33 [6]. Ed and Em stand for the elastic moduli of the dendrites and glass matrix, respectively. Eq. (1) can be rewritten as: cd ¼
Ed : 0:71Ed þ 0:29Em
ð2Þ
It is known that the shear deformation of BMGs is closely related with the creation and annihilation of free volumes [36]. If the annihilation rate is smaller than the creation rate, the growth of the average free volumes is controlled by the deformation. For a uniaxial test at a constant strain rate of ε0 , the increased average free volumes are given as [36]:
V 2f −V 20 ¼ 2α 1 ε0 t
ð3Þ
where V0 is the average free volume at the load-free condition, Vf is the average free volumes of an atom, t stands for time, and α1 is a function of the temperature: pffiffiffi 2 3αV NvRT α1 ¼ χ Na S
ð4Þ
where α is a constant between 1 and 0.5, V ∗ is the effective hard-sphere size of atoms, χ is a factor associated with the amount of the flow units, N is the total number of atoms, v is the frequency of atomic vibration, Na 1þv is the Avogadro constant, R is the gas constant, and S ¼ 23 μ 1−v , μ is shear modulus, and v is Poisson's ratio. Combining Eqs. (3) and (4), the increased average free volumes are given as: V 2f −V 20 ¼
pffiffiffi 4 3αV NvR ε0 tT: χ Na S
ð5Þ
From Eq. (5), the free volumes grow during the plastic deformation, which has been verified by experiments [20,21,24–26] and modelings [23]. Thus, the annihilation rate is smaller than the creation rate upon deformation. The increased free volumes will lead to the decrease of the Young's modulus of the glass matrix [20,24,25], while, the elastic modulus of the dendrites will keep constant [25]. From Eq. (2), before compressive deformation, the values of average stress concentration factors of the dendrites in samples B and C are increased compared with that in sample A. Once the concentrative stress exceeds the yielding stress of the dendrites, the plastic deformation occurs. According to the Taylor dislocation model [37], the stress–strain relation of the dendrites during plastic deformation is given as:
σ d ¼ σ re f
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2n σ yd =Ed þ εpd þ Lη
ð6Þ
where σref is the reference stress of the dendrites under uniaxial tension, n−1 . Here, n is the hardening coefficient of 0.07 [38], Ed and σref = End/σyd is the Young's modulus of 106.3 GPa [39], σd is suggested to be 1336 MPa [40], εpd is the plastic strain of the dendrites, and Lη stands for the contribution to the work hardening from geometrically necessary dislocations. L is the intrinsic material length of the dendrites, and L = 180b(aμ/σref)2. μ and b are the shear modulus and Burgers vector of the dendrites, and μ ¼ Ed 2ð1þv Þ . Assumed that the Burgers vector d
of the dendrites, b, is about 1 nm [41]. a is an empirical material constant in the Taylor dislocation model with a value of 0.3 [42]. η is the effective plastic-strain gradient, which can be replaced by an average plastic strain gradient, η. Here, η ¼ η ¼ εd =D, where D is the average diameter
269
of the dendrites with a value of ~2 μm, as shown in Fig. 1(B). Eq. (6) can be rewritten as: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:14 σ d ¼ 690:2 0:01 þ εpd þ 6εpd :
ð7Þ
As the dendrites yield, the relationship between the tensile strain of composite, εc, and that of the dendrites is given as [43]: εc ¼ f v cd εd :
ð8Þ
A simple rule of mixture is employed as a first-order approximation to evaluate the axial stress of the composite, σc: σ c ¼ f v σ d þ ð1−f v Þσ m :
ð9Þ
From Eqs. (7), (8), and (9), the stress–strain relationship at the plastic deformation stage can be expressed as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2:2ε c 0:14 13:2ε c 0:01 þ þ þ 0:54σ m : cd cd
σ c ¼ 317:5
ð10Þ
From Eq. (10), on the condition of the same stresses, σc, the larger average stress concentration factor of the dendrites, the larger fracture strain of the composite is. Based on Eq. (2), the average stress concentration factor is increased for samples after tensile pre-deformation. In addition, the larger average stress concentration factor of the dendrites, the more dense shear bands will be initiated. Consequently, the fracture strains of samples B and C are larger than that of sample A, which agrees with the shear-band density on the lateral surface, i.e. the shear-band density of B and C is larger than that of sample A, as shown in Fig. 5. Fig. 5 reveals the morphologies of the fracture and lateral surfaces of the deformed samples. The primary shear bands with a large average spacing of ~9 μm, along the parallel direction with respect to the fracture plane, distribute on the side surface of sample A, as shown in Fig. 5(a). While for sample B, profuse shear bands with a fine average spacing of about 3 μm distribute over the entire side surface, characterized as a regular array, shown in Fig. 5(b), and these shear bands are approximately parallel to the fracture plane. The lateral surface of deformed sample C is displayed in Fig. 5(c). It is observed that the primary shear bands with an average spacing of ~3 μm, and the branched and winding secondary shear bands appear among the primary shear bands. It may originate from the impediment of the β-Ti dendrites to the propagation of shear bands [44]. The fracture surface of deformed samples A, B, and C is similar, and the fracture surface of sample C is illustrated in Fig. 5(d). The droplet-like patterns, related to the melting, are detected on the fracture surface, and the frictional sliding causes a temperature burst sufficiently high to provoke local melting even before fracture [45]. For the current composites, after yielding, the strain energy, accumulated during the plastic deformation, can be partly converted to heat, leading to temperature rise so that the fracture surface would receive more energy [46]. It should be noted that the intrinsic difference is weak between samples B and C, since sample C is far away from the necking region. Wu et al. [47] have reported that MGMCs usually experienced inhomogeneous deformation with strong necking or strain localization after yielding. Meanwhile, the true stress at the necking part after correction is larger than that reflected from the stress–strain curve [47]. Thus, it should be considered that the deformation mechanism in sample C is similar to that in sample B. In addition, the similarity has been verified by the approaching values of the average spacing of the primary shear bands between samples B and C, as shown in Fig. 5(b) and (c). In other words, the average spacing of the primary shear bands is increased orderly in samples A, C, and B, in agreement with the plasticity in Fig. 4, indicating that the plasticity of MGMCs can be improved by tensile pre-deformation. The multiplication of shear bands attributes to the decrease of the Young's modulus of the glass matrix.
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Fig. 5. The lateral surfaces of the compressive deformed samples A, B, and C shown in (a), (b), and (c), respectively. The fracture surface of sample C in (d).
Besides, from Eq. (2), the stress concentration factor is: cd ¼
1 0:71 þ 0:29
Em Ed
:
in in-situ dendrite-reinforced MGMCs opens a door to design MGMCs with excellent plasticity. ð11Þ
In order to improve the plasticity, the stress concentration factor must be large. In general, for in-situ dendrite-reinforced MGMCs, the Young's modulus of the glass matrix is larger than that of the dendrites [4,21,48, 49], i.e., Em ≥ Ed or EEmd ≥1. Therefore, the stress concentration factor is: cd ¼
1 0:71 þ 0:29
Em Ed
≤1:
ð12Þ
When Em = Ed, the stress concentration factor is the largest with a value of 1, and the composite can achieve the largest plasticity. Actually, Ed hardly matches Em naturally. In the current investigation, the Young's modulus of the glass matrix is tailored, and the remarkable plasticity of MGMCs is achieved by tensile pre-deformation. The plasticity of in-situ MGMCs can be improved by predeformation, as the free volumes in the glass matrix will increase. Moreover, the tailored Young's modulus of the dendrites improves the plasticity. For example, the Young's modulus of the B2 phase in the as-cast composite is measured to be 107.3 GPa by nanoindentation, slightly smaller than that of the glass matrix of 108.2 GPa, which enables attraction and/or arrest of shear bands by the crystalline phases, as explained before by Hofmann et al. [4,6]. As a result, the B2 reinforced MGMCs yield excellent plasticity [4,6]. The experimental result is verified by Wu et al. [50]. In other words, matching Young's modulus of dual phases
5. Conclusion In this study, the tensile pre-deformation and compressive tests are conducted to investigate the mechanical behavior of MGMCs. It is found that the compressive strains of specimens after tensile pre-deformation are roughly 30%–50%, greatly higher than that of an as-cast one. The tensile pre-deformation leads to the increasing of free volumes in the glass matrix, resulting in the Young's modulus of the glass matrix decreasing. The decreased Young's modulus of the glass matrix matches the Young's modulus of the dendrites after tensile pre-deformation, yielding an excellent plasticity. When Young's modulus of the dendrites is equal to that of the glass matrix for the present MGMCs, the plasticity is achieved to be the largest. Matching Young's modulus of dual phases opens a door to design in-situ dendrite-reinforced MGMCs with excellent plasticity. Acknowledgments J.W.Q. would like to acknowledge the financial support of the National Natural Science Foundation of China (no. 51371122), the Program for the Innovative Talents of Higher Learning Institutions of Shanxi (2013), and the Youth Natural Science Foundation of Shanxi Province, China (no. 2015021005). H.J.Y. would like to acknowledge the financial support from the National Natural Science Foundation of China (no. 51401141) and the Youth National Science Foundation of Shanxi Province, China (no. 2014021017-3). Z.H.W. would like to acknowledge the National Natural Science Foundation of China (no. 11390362).
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Plasticity improvement for dendrite/metallic glass matrix composites by pre-deformation X.H. Sun a,b, Y.S. Wang a,b, J. Fan a, H.J. Yang c, S.G. Ma d, Z.H. Wang d, J.W. Qiao a,b,⁎ a
Laboratory of Applied Physics and Mechanics of Advanced Materials, College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China Key Laboratory of Interface Science and Engineering in Advanced Materials, Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan 030024, China d Institute of Applied Mechanics and Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, China b c
a r t i c l e
i n f o
Article history: Received 11 May 2015 Received in revised form 8 July 2015 Accepted 19 July 2015 Available online 26 July 2015 Keywords: Metallic glass Composite Improved plasticity Tensile pre-deformation Shear bands Young's modulus
a b s t r a c t The mechanical properties of in-situ metallic glass matrix composites (MGMCs) are investigated by tensile predeformation, followed by compression. The pre-deformation is utilized to exploit notable increases in plasticity, accompanied by slight increases in the compressive strength, and the deformation mechanisms are explored. The increased free volumes in the glass matrix after tensile pre-deformation contribute to the decrease of the Young's modulus of the glass matrix and lead to the increase in the stress concentration, promoting multiplication of shear bands. When the Young's modulus of the glass matrix matches that of the dendrites, the plasticity of insitu dendrite-reinforced MGMCs is the optimized. Matching Young's modulus opens a door to design the MGMCs with excellent plasticity and remarkable work-hardening capability. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Plastic deformation in bulk metallic glasses (BMGs) manifests through the strain localization shearing into narrow bands, which are often referred to as shear bands [1,2]. The shear bands, which have an unhindered propagation in monolithic BMGs, yield negligible tensile ductility. Recently, great interest arises in BMGs as structural materials, since they exhibit superior mechanical properties, such as high strength, large elastic limits, and high corrosion resistance [3]. However, a widespread acceptance of monolithic BMGs in engineering applications is limited by their poor ductility under loading at room temperature. One way to alleviate this problem is that the crystalline phases are insitu introduced to effectively generate multiple shear bands and impede the rapid propagation of shear bands [4,5]. To date, the dimension for lightweight in-situ dendrite-reinforced metallic glass matrix composites has reached a centimeter scale and even larger for systems such as Ti–Zr–V–Cu–Be [6], Ti–Zr–Ni–Cu–Be [7], and Ti–Zr–Cu–Ni–Al [8]. These ingots are large enough to be used as potential structural materials in various application fields. It should be noted that the improvement of plasticity and the enhancement of work-hardening capacity are badly needed for dendrite-reinforced metallic glass matrix composites (MGMCs). ⁎ Corresponding author at: Yingze West Street 79 Taiyuan, Shanxi Province, 030024, China. Tel.: +8613643467172. E-mail address: [email protected] (J.W. Qiao).
http://dx.doi.org/10.1016/j.matdes.2015.07.109 0264-1275/© 2015 Elsevier Ltd. All rights reserved.
For in-situ MGMCs, the deformation mechanisms should be fully understood before actual service. After introducing the secondary phases in the glass matrix, both phases in the composites are under the multi-axial stress state during the deformation. The concentrated stress, induced by the secondary phases, can interact with the stress field, originated from propagating shear bands, leading to the multiplication, branching, and deflection of shear bands. As a result, shear bands in these MGMCs are characterized to be dense, short, and wavy [9]. The profuse shear bands could accommodate more strain energy, resulting in effective toughening. For monolithic BMGs, introducing structural inhomogeneity can produce residual stress, and then, the pre-existed shear bands and free volumes improve the plasticity [10–12]. Zhang et al. [10] have pointed out that the plasticity of Vitreloy 1 BMGs was improved by introducing compressive residual stress on the sample surface by shot-peening. Cao et al. [11] have reported that pre-existed properly-spaced soft inhomogeneities can stabilize shear bands and lead to tensile ductility, and the effective intersection of shear bands in conjugated directions resulted in obvious work hardening. Haruyama et al. [12] put forward that coldrolled BMGs exhibited volume dilatation, caused by the generation of free volumes. Generally, the heterogeneities can manipulate nucleation and propagation of shear bands, which is responsible for the enhanced plasticity of BMGs [13]. Hofmann et al. [14] have reported that the shear bands generated during rolling provided nucleation sites for the new shear bands generated during tension. The deformation mechanisms of β-Ti solid solution (dendrites) are based on the dislocation
X.H. Sun et al. / Materials and Design 86 (2015) 266–271
multiplication and slip [15–18]. The work-hardening capacity, associated with homogeneous deformation, is highly dependent on the large plastic deformation of both the dendrites and the metallic glass matrix [19]. Based on the above micromechanisms, multiplication, branching, and deflection of the shear bands are crucial to improve the plasticity. The pre-deformation not only increases the free volumes in the glass matrix [12,20–25], but also the dislocation density within the crystalline dendrites increases [15–18]. Recently, Ke et al. reported [26] that the Zr46.75Ti8.25Cu7.5Ni10Be27.5 BMG exhibited volume dilatation of up to 0.2% after compressive creep of the as-cast sample at a yield stress of 80%, and this phenomenon is attributed to the generation of a great amount of free volumes. The increased free volumes make the Young's modulus of the glass matrix decrease [20,24,25], resulting in the Young's modulus of the glass matrix and dendrites being approaching, since the crystalline dendrites have a lower Young's modulus than the glass matrix. The aim of this study is to investigate the contribution of matching the Young's modulus between the glass and dendrite phases to the plasticity of in-situ dendrite-reinforced MGMCs. 2. Experimental procedures Ingots of a nominal composition: Ti48Zr18V12Cu5Be17 (at.%) were prepared by arc-melting a mixture of the elements Ti, Zr, V, Cu, and Be with high purity (N99.9%) under a Ti-gettered argon atmosphere. Two cylindrical rods with a diameter of 2 mm and 6 mm were prepared via suction casting into a copper mold, respectively. The phases of the samples were checked by X-ray diffraction (XRD) in a Philips APD-10 diffractometer with Cu Ka radiation. The pre-deformation experimental procedures were schematically shown in Fig. 1. The dog-bone-like tensile samples with a nominal diameter of 2 mm and a length of 15 mm were machined from the as-cast rods with 6-mm diameter. Sample A with an aspect ratio of 2:1 was cut from the gage section of as-cast samples, and their ends were prepared and polished to ensure the parallelism. The tensile samples were drawn to the stage of work hardening and the failure at room temperature at a constant strain rate of 5 × 10−4 s−1, respectively. And then, samples B and C with an aspect ratio of 2:1 were cut from the deformed samples within the gage section, respectively, as shown in Fig. 1. Sample D with an aspect ratio of 2:1 was directly cut from as-cast bars with a diameter of 2 mm. The compressive tests were carried out on samples A, B, C, and D at a strain rate of 5 × 10−4 s−1. The microstructures of as cast samples and the fracture
Fig. 1. The experimental procedure schematic diagram.
267
surfaces after compression were investigated by scanning electron microscopy (SEM). 3. Results 3.1. Microstructures The microstructures of samples D and A are illustrated in Fig. 2(a) and (b), respectively. The SEM images of the cross-sections for samples B and C are very similar to that of sample A (not shown). The dense small dendrites are homogeneously embedded in the glass matrix, as shown in Fig. 2(a). From the magnified image in the inset of Fig. 2(a), the average diameter of the dendritic arms of sample D is less than 1 μm. However, that of samples A, B, and C are the same with a value of ~ 2 μm, as shown in Fig. 2(b). The size of the dendritic arm can be controlled by the cooling rate during casting [27]. The dendrite's volume fractions in samples A, B, C, and D are all ~46% by analyzing the contrast of the SEM image, and similar results have been observed by Jeon et al. [28]. X-ray diffraction patterns of the composites (not shown here) indicate that the dendritic phase is a β-Ti solid solution with a body-centered cubic crystal structure. 3.2. Mechanical behavior 3.2.1. Tensile behavior Fig. 3 displays the tensile stress–strain curve of the present composites. After yielding, the MGMCs exhibit not only high tensile strength of 1422 MPa, but also remarkable work-hardening capacity. The following softening dominates until the final fracture at a fracture strain of ~5.9%.
Fig. 2. The SEM micrographs of the as-cast composites with a diameter of 2 mm and 6 mm in (a) and (b), respectively. The inset of (a) being magnified micrograph of as-cast composite with a diameter of 2 mm.
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X.H. Sun et al. / Materials and Design 86 (2015) 266–271 Table 1 Summary of compressive yielding strength (σy), elastic strain (εy), ultimate compressive strength (σmax), and total strain to failure (εf) for the present MGMCs. Sample
A B C D
σy
εy
σmax
εf
MPa
%
MPa
%
1675 1493 1646 2026
1.98 1.93 1.96 1.99
2585 2747 2697 2815
22.9 34.6 30.3 19.2
A: Φ6 → 2 casting. B: Φ6 → 2 hardening. C: Φ6 → 2 softening. D: Φ2 casting.
4. Discussion Fig. 3. The tensile true stress–strain curve of as-cast Ti48Zr18V12Cu5Be17 sample. The samples in pictures (i), (ii), and (iii) being in a state of casting, work hardening, and softening, respectively. The inset (iv) showing the lateral surface near the necked region after tension failure.
Macroscopic necking can be observed in the inset (iii), in agreement with the large tensile ductility. Samples A, B, and C are machined from the tensile specimens, as exhibited in the insets of (i), (ii), and (iii) in Fig. 3, respectively. The inset (iv) in Fig. 3 shows the lateral surface near the necking region after failure. Multiplication of shear bands within the glass matrix, indicated by the dark arrows, together with some cracks, indicated by the light arrows, is consistent with the distinguished tensile ductility.
3.2.2. Compressive behavior Fig. 4 represents the compressive stress–strain curves of samples A, B, C, and D. Initially perfectly elastic deformation is followed by the obvious macroscopic plastic deformation. Summary of compressive mechanical properties is listed in Table 1. Sample D possesses the highest yielding strength of 2026 MPa, but the lowest plasticity of 19.2%. Sample A exhibits lower yielding strength of 1675 MPa and larger plasticity of 22.9%, similar results that improved plasticity at the expense of yielding stress have been found in samples DH1, DH2, and DH3 [4]. Compared with sample A, the difference exists in yielding stress, and the fracture strain of sample C is 32% higher than that in sample A. Sample B at a state of work hardening has larger plasticity but lower yielding stress than sample C at a state of softening. The slight increases in the ultimate compressive strength for samples B and C with the pre-tension deformation, and the analogical results are found in pre-rolled MGMCs [14].
Most monolithic BMGs exhibit catastrophic failure with brittleness upon whether tensile or compressive loadings at room temperature, as dominated by individual shear bands, since large plasticity is usually correlated to profuse shear bands [11–15,29]. For the conventional crystalline samples, the macroscopic plasticity is closely related to the multiplication of dislocations [18]. As far as the current composite is concerned, the deformation mechanisms of the glass matrix and crystalline dendrites are coupled upon quasi-static compression. Different sizes of the dendrites lead to different mechanical properties, and the size of the dendrites plays an important role in gaining the ductility of in-situ MGMCs [4,6,30]. The crystalline phases can absorb the strain energy during the deformation, contributing to the improved plasticity. Besides, the propagation of shear bands can be arrested by the ductile crystalline phases, the instability can be suppressed, and the significantly improved toughness of MGMCs at room temperature prevails. However, not all the dendrites, dispersed in metallic glass matrix, can initiate and arrest shear bands, and finally lead to the formation of profuse shear bands. The size of the dendrites is too small to retard the rapid propagation of shear bands, accompanied by a decreasing plasticity [27,31]. As the stress is increased, more shear transformation zones (STZs) within the glass matrix will be activated. When the stress reaches a critical value, yielding occurs to produce plastic deformation, immediately followed by the initiation of shear bands [32]. At the plastic deformation stage, the shear bands initiate in the glass matrix, the larger stress concentration will stimulate more shear bands near the interface. As a result, the plasticity of the composites is enhanced. But for the present sample D, the dendrites are so small that the maximum stress concentration happens at the elastic stage [30], while the glass matrix is still under elastic deformation and strong enough to impede the initiation of shear bands. At the plastic stage, the stress concentration becomes weak, which cannot induce generations of shear bands. Macroscopically, sample D is less plastic than sample A with large-sized dendrites, and similar results have been obtained in in-situ Ti-based [33] and Zr-based MGMCs [27]. The ductile dendrites are confined by the glass matrix, which experience a multi-axial stress state and produce inhomogeneous plastic deformation upon compression [34]. The strong interfacial bonding effectively transfers the stress to the matrix [33]. Therefore, the stress concentration within dendrites produced by plastic deformation will lead to the initiation of shear bands in the glass matrix near the interface, and the stress concentration factors of the dendrites will affect the initiation of shear bands. The average stress concentration factors of the dendrites can be described as follows [35]: cd ¼
Fig. 4. The compressive stress–strain curves of the present samples with different pretreatments.
Ed ½ f v þ ð1−f v ÞβðEd −Em Þ þ Em
ð1Þ
where fv represents the volume fraction of the dendrites with a value of 0.46, cd represents the average stress concentration factors of the
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dendrites, β is the material constant, which is calculated through β ¼ 8−10vd 15ð1−vd Þ ,
and vd is the Poisson's ratio of the dendrites with a value of
0.33 [6]. Ed and Em stand for the elastic moduli of the dendrites and glass matrix, respectively. Eq. (1) can be rewritten as: cd ¼
Ed : 0:71Ed þ 0:29Em
ð2Þ
It is known that the shear deformation of BMGs is closely related with the creation and annihilation of free volumes [36]. If the annihilation rate is smaller than the creation rate, the growth of the average free volumes is controlled by the deformation. For a uniaxial test at a constant strain rate of ε0 , the increased average free volumes are given as [36]:
V 2f −V 20 ¼ 2α 1 ε0 t
ð3Þ
where V0 is the average free volume at the load-free condition, Vf is the average free volumes of an atom, t stands for time, and α1 is a function of the temperature: pffiffiffi 2 3αV NvRT α1 ¼ χ Na S
ð4Þ
where α is a constant between 1 and 0.5, V ∗ is the effective hard-sphere size of atoms, χ is a factor associated with the amount of the flow units, N is the total number of atoms, v is the frequency of atomic vibration, Na 1þv is the Avogadro constant, R is the gas constant, and S ¼ 23 μ 1−v , μ is shear modulus, and v is Poisson's ratio. Combining Eqs. (3) and (4), the increased average free volumes are given as: V 2f −V 20 ¼
pffiffiffi 4 3αV NvR ε0 tT: χ Na S
ð5Þ
From Eq. (5), the free volumes grow during the plastic deformation, which has been verified by experiments [20,21,24–26] and modelings [23]. Thus, the annihilation rate is smaller than the creation rate upon deformation. The increased free volumes will lead to the decrease of the Young's modulus of the glass matrix [20,24,25], while, the elastic modulus of the dendrites will keep constant [25]. From Eq. (2), before compressive deformation, the values of average stress concentration factors of the dendrites in samples B and C are increased compared with that in sample A. Once the concentrative stress exceeds the yielding stress of the dendrites, the plastic deformation occurs. According to the Taylor dislocation model [37], the stress–strain relation of the dendrites during plastic deformation is given as:
σ d ¼ σ re f
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2n σ yd =Ed þ εpd þ Lη
ð6Þ
where σref is the reference stress of the dendrites under uniaxial tension, n−1 . Here, n is the hardening coefficient of 0.07 [38], Ed and σref = End/σyd is the Young's modulus of 106.3 GPa [39], σd is suggested to be 1336 MPa [40], εpd is the plastic strain of the dendrites, and Lη stands for the contribution to the work hardening from geometrically necessary dislocations. L is the intrinsic material length of the dendrites, and L = 180b(aμ/σref)2. μ and b are the shear modulus and Burgers vector of the dendrites, and μ ¼ Ed 2ð1þv Þ . Assumed that the Burgers vector d
of the dendrites, b, is about 1 nm [41]. a is an empirical material constant in the Taylor dislocation model with a value of 0.3 [42]. η is the effective plastic-strain gradient, which can be replaced by an average plastic strain gradient, η. Here, η ¼ η ¼ εd =D, where D is the average diameter
269
of the dendrites with a value of ~2 μm, as shown in Fig. 1(B). Eq. (6) can be rewritten as: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:14 σ d ¼ 690:2 0:01 þ εpd þ 6εpd :
ð7Þ
As the dendrites yield, the relationship between the tensile strain of composite, εc, and that of the dendrites is given as [43]: εc ¼ f v cd εd :
ð8Þ
A simple rule of mixture is employed as a first-order approximation to evaluate the axial stress of the composite, σc: σ c ¼ f v σ d þ ð1−f v Þσ m :
ð9Þ
From Eqs. (7), (8), and (9), the stress–strain relationship at the plastic deformation stage can be expressed as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2:2ε c 0:14 13:2ε c 0:01 þ þ þ 0:54σ m : cd cd
σ c ¼ 317:5
ð10Þ
From Eq. (10), on the condition of the same stresses, σc, the larger average stress concentration factor of the dendrites, the larger fracture strain of the composite is. Based on Eq. (2), the average stress concentration factor is increased for samples after tensile pre-deformation. In addition, the larger average stress concentration factor of the dendrites, the more dense shear bands will be initiated. Consequently, the fracture strains of samples B and C are larger than that of sample A, which agrees with the shear-band density on the lateral surface, i.e. the shear-band density of B and C is larger than that of sample A, as shown in Fig. 5. Fig. 5 reveals the morphologies of the fracture and lateral surfaces of the deformed samples. The primary shear bands with a large average spacing of ~9 μm, along the parallel direction with respect to the fracture plane, distribute on the side surface of sample A, as shown in Fig. 5(a). While for sample B, profuse shear bands with a fine average spacing of about 3 μm distribute over the entire side surface, characterized as a regular array, shown in Fig. 5(b), and these shear bands are approximately parallel to the fracture plane. The lateral surface of deformed sample C is displayed in Fig. 5(c). It is observed that the primary shear bands with an average spacing of ~3 μm, and the branched and winding secondary shear bands appear among the primary shear bands. It may originate from the impediment of the β-Ti dendrites to the propagation of shear bands [44]. The fracture surface of deformed samples A, B, and C is similar, and the fracture surface of sample C is illustrated in Fig. 5(d). The droplet-like patterns, related to the melting, are detected on the fracture surface, and the frictional sliding causes a temperature burst sufficiently high to provoke local melting even before fracture [45]. For the current composites, after yielding, the strain energy, accumulated during the plastic deformation, can be partly converted to heat, leading to temperature rise so that the fracture surface would receive more energy [46]. It should be noted that the intrinsic difference is weak between samples B and C, since sample C is far away from the necking region. Wu et al. [47] have reported that MGMCs usually experienced inhomogeneous deformation with strong necking or strain localization after yielding. Meanwhile, the true stress at the necking part after correction is larger than that reflected from the stress–strain curve [47]. Thus, it should be considered that the deformation mechanism in sample C is similar to that in sample B. In addition, the similarity has been verified by the approaching values of the average spacing of the primary shear bands between samples B and C, as shown in Fig. 5(b) and (c). In other words, the average spacing of the primary shear bands is increased orderly in samples A, C, and B, in agreement with the plasticity in Fig. 4, indicating that the plasticity of MGMCs can be improved by tensile pre-deformation. The multiplication of shear bands attributes to the decrease of the Young's modulus of the glass matrix.
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Fig. 5. The lateral surfaces of the compressive deformed samples A, B, and C shown in (a), (b), and (c), respectively. The fracture surface of sample C in (d).
Besides, from Eq. (2), the stress concentration factor is: cd ¼
1 0:71 þ 0:29
Em Ed
:
in in-situ dendrite-reinforced MGMCs opens a door to design MGMCs with excellent plasticity. ð11Þ
In order to improve the plasticity, the stress concentration factor must be large. In general, for in-situ dendrite-reinforced MGMCs, the Young's modulus of the glass matrix is larger than that of the dendrites [4,21,48, 49], i.e., Em ≥ Ed or EEmd ≥1. Therefore, the stress concentration factor is: cd ¼
1 0:71 þ 0:29
Em Ed
≤1:
ð12Þ
When Em = Ed, the stress concentration factor is the largest with a value of 1, and the composite can achieve the largest plasticity. Actually, Ed hardly matches Em naturally. In the current investigation, the Young's modulus of the glass matrix is tailored, and the remarkable plasticity of MGMCs is achieved by tensile pre-deformation. The plasticity of in-situ MGMCs can be improved by predeformation, as the free volumes in the glass matrix will increase. Moreover, the tailored Young's modulus of the dendrites improves the plasticity. For example, the Young's modulus of the B2 phase in the as-cast composite is measured to be 107.3 GPa by nanoindentation, slightly smaller than that of the glass matrix of 108.2 GPa, which enables attraction and/or arrest of shear bands by the crystalline phases, as explained before by Hofmann et al. [4,6]. As a result, the B2 reinforced MGMCs yield excellent plasticity [4,6]. The experimental result is verified by Wu et al. [50]. In other words, matching Young's modulus of dual phases
5. Conclusion In this study, the tensile pre-deformation and compressive tests are conducted to investigate the mechanical behavior of MGMCs. It is found that the compressive strains of specimens after tensile pre-deformation are roughly 30%–50%, greatly higher than that of an as-cast one. The tensile pre-deformation leads to the increasing of free volumes in the glass matrix, resulting in the Young's modulus of the glass matrix decreasing. The decreased Young's modulus of the glass matrix matches the Young's modulus of the dendrites after tensile pre-deformation, yielding an excellent plasticity. When Young's modulus of the dendrites is equal to that of the glass matrix for the present MGMCs, the plasticity is achieved to be the largest. Matching Young's modulus of dual phases opens a door to design in-situ dendrite-reinforced MGMCs with excellent plasticity. Acknowledgments J.W.Q. would like to acknowledge the financial support of the National Natural Science Foundation of China (no. 51371122), the Program for the Innovative Talents of Higher Learning Institutions of Shanxi (2013), and the Youth Natural Science Foundation of Shanxi Province, China (no. 2015021005). H.J.Y. would like to acknowledge the financial support from the National Natural Science Foundation of China (no. 51401141) and the Youth National Science Foundation of Shanxi Province, China (no. 2014021017-3). Z.H.W. would like to acknowledge the National Natural Science Foundation of China (no. 11390362).
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